Ginna and her daughter had bounced from couch to couch for months before they lost their last refuge: A friend, worried about losing her lease, asked her to leave.

Unemployed and out of options, the young mother went to the state to ask for emergency shelter on Aug. 8. She had previously been denied because she was $12 over the income limit. Now Department of Housing and Community Development workers suspected Ginna of quitting her job at a sandwich shop to get benefits. She begged them to talk to her former boss, who could tell them she was let go because she had no child care and couldn’t make shifts. They didn’t.

“If only they had made that call, this would never, ever have happened to me,” said the slight, dark-haired 21-year-old.

Instead, Ginna and her 17-month-old began sleeping at South Station. On the first night, a man brought her food. He came back the next night and told her he had a place for her to stay. She was exhausted and her baby was wailing and she had no one, so she went with him. Later that night, the man raped her. She waited for him to fall asleep, then fled with her daughter.

David L. Ryan/Globe Staff

“I work, I don’t party, I don’t do drugs. I’m a good girl. I want to make something of myself,” Ginna, a rape victim who was turned away from homeless shelter.

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The Patrick administration’s heart might be in the right place when it comes to ending homelessness, but its new approach to this huge problem is hurting some of the very people most in need of help. While boosting resources for permanent housing, the state has begun turning away an alarming number of families from its shelter system. Until recently, 40 to 50 percent of families who applied for emergency shelter were denied each month. Last month, the average was 68 percent. In the last week of September, 74 percent of families seeking shelter were denied. Ginna’s case is the most tragic of many.

“We’ve seen a real spike,” said Jim Greene, director of Boston’s Emergency Shelter Commission, which took about 500 calls from desperate families last month, compared to an average of 375 earlier this year. “We get calls almost daily . . . reporting that people are staying in emergency rooms because they have nowhere else to go. More people are reporting to us that they’re staying in parks and vans.” Boston Medical Center confirms that it has seen an increase in homeless families showing up at the ER over the last month.

“We are completely inundated” with calls from families who have nowhere to go, said Ruth Bourquin, senior attorney at the Massachusetts Law Reform Institute. “Before August, we almost never heard of families staying in [cars]. Now it’s every day.”

Since new regulations went into effect in August, state workers are suddenly far more skeptical about people’s claims of homelessness, far less likely to believe somebody who says they can no longer stay with the friend or grandmother with whom they’ve been doubled up.

“The restrictions have never been this tough before,” said Kelly Turley, legislative director of the Massachusetts Coalition for the Homeless. “This is the most discouraging situation I’ve seen. It’s scary.”

How did we get here? From good intentions, actually. The Patrick administration and many legislators are truly committed when it comes to the issue of homelessness. Currently, the state provides shelter space to about 2,000 families, and houses another 1,800 in expensive motels. Few other states provide that kind of safety net.

In an effort to move people out of politically unpopular motels and head off homelessness before it happens, the 2013 budget contains big funding increases for rental assistance and other programs that keep struggling families in their homes. Accompanying the shift towards permanent housing are the new regulations designed to make getting into shelters more difficult.

“Obviously we want to maintain a strong safety net,” said Aaron Gornstein, undersecretary for Housing and Community Development. “But we also want to make sure we’re spending taxpayer dollars wisely, investing in prevention and permanent housing, and that emergency shelter is a last resort.”

The problem is, there isn’t yet enough prevention and affordable housing to save many families from the street. “None of us have a safety net to put under the safety net that has been restricted,” said Greene.

What’s frustrating to him, and to others who work on the front lines, is that the state seems unwilling to recognize there is a problem here. State officials seem entirely wedded to the notion that almost everybody has somewhere to stay, even when they say they don’t. They say this is based on experience – that their past investigations have shown people can almost always find someone to take them in.

‘I work, I don’t party, I don’t do drugs.I’m a good girl. I want to makesomething of myself.’

They’re not persuaded by the stories of families sleeping in cars and on beaches and in the lobbies of apartment buildings, which they believe are exaggerated by advocates determined to grow the shelter system. Privately, they have suggested Greene and others are using poor families as pawns. Publicly, they wonder if advocates are suggesting homeless families put themselves in dangerous situations just to qualify for shelter.

“I hope they’re not coaching them to do that,” Gornstein said.

Seriously? People who have devoted careers to ending homelessness would advise families to give up homes and put themselves in harm’s way?

It’s hard to reconcile the Deval Patrick who demanded that his party stop apologizing for its values at the Democratic National Convention with the way his administration is handling this.

“I believe the governor when he said it’s about our values,” said Senator Ken Donnelly, an Arlington Democrat who is one of a group of legislators trying to rebalance the shelter regulations. “But they have this feeling that people are somehow gaming the system, and you just look at them and say, ‘What planet are you on?’ ”

Look, this is clearly a tough issue. The governor and the Legislature have taken on a difficult and expensive balancing act trying to work out how much to devote to long-term solutions like affordable housing and how much to short-term ones like shelter. It is always a good idea to keep people with family or friends as they await help with permanent housing — as long as that is possible. But the state is increasingly unwilling to admit that sometimes, it’s not. And some of the very people shelters are designed to protect are casualties.

“I work, I don’t party, I don’t do drugs,” Ginna said. “I’m a good girl. I want to make something of myself.”

When she went back to the housing office in Roxbury after she was raped, Ginna said, housing officials refused to look at her rape kit. They denied her shelter again, then had her escorted out by guards, she said. Then the workers who had refused Ginna and her daughter a safe place to sleep filed a report accusing her of neglecting her baby.

Gornstein said Ginna’s shelter denials had nothing to do with the new, stricter regulations. He said she would have been denied last year, too, because workers believed she had quit her job without good cause.

No way, say those who have been fighting for Ginna: They’re certain she would have gotten the benefit of the doubt before, that workers would have made the call to her supervisor.

That would have taken three minutes, tops. Last week, that supervisor, Robert Peebles, picked up on the second ring at the cell number Ginna begged state workers to call in August. He said he never received a call or a message from housing workers. Ginna lost her job “because she couldn’t make it any more, she had her daughter and she was not able to obtain child care,” he confirmed. A second call to the sandwich shop to confirm Peebles was a supervisor there took another minute.

In an affidavit, a Department of Housing and Community Development supervisor said a worker in the Dudley Square office did try Peebles’s cell at some point, but did not speak to him. Ginna said the worker certainly didn’t call while she was pleading with her in the office.

“While she was sleeping in her bed, I was being raped,” she said. “That’s going to be with me for the rest of my life. Nobody can erase this.”

Still, Ginna is trying to move on. The sandwich shop hired her back last week. She is working on finding care for her daughter so she can pick up more hours. She wants to get into her own place quickly, to stabilize her life so she can bring her husband from the Dominican Republic; she is a US citizen.

Gornstein said he is looking into Ginna’s case, and at those of other families across the state who advocates say have been unfairly denied shelter under the new rules. “I want to assure you, we are taking this very seriously to make sure people don’t fall through the cracks,” Gornstein said. “We’re trying to err on the side of caution and make sure we maintain a safety net for people who really need it.”

There will be hearings on the new shelter regulations in Western Massachusetts on Oct. 22, and in Boston on Oct. 25. Ginna may testify. Gornstein points out that his office has already made 20 changes to the new rules based on public input, and that it’s prepared to make more to better protect families who need help.